Pseudo-Lorenz attractors in echo state networks

Abstract This study investigates attractor reconstruction via reservoir computing, focusing on how the reservoir’s structural constraints influence the learned dynamics. As a case study, we analyze the state space of a standard echo state network (ESN) trained to reconstruct the Lorenz system. As model parameters vary, the reconstructed attractor undergoes crises and decomposes into two spiral structures divided by a saddle point—an artifact absent in the original Lorenz system. This phenomenon suggests that the ESN forms a pseudo-Lorenz double-spiral attractor, which can be interpreted as a manifestation of the reservoir’s intrinsic constraints, such as symmetry and nonlinearity. The interaction between such constraints and the teacher data is an inherent aspect of the attractor reconstruction task by reservoir computing.